Many mathematically talented people I know (those who perform well in the International Mathematical Olympiad (IMO) or the Putnam competition) go into derivatives trading and finance simply because a) it's mathematically challenging b) there are answers and rewards for getting things "right" (you get more money) c) it's competitive (some of these are zero-sum games played against other intelligent market actors). I am curious as to fields they could join that would mimic this environment, but be highly impactful?